In such a process, which is known from German Patent Specification 3,800,201, the CO.sub.2 content of the waste air is used as a measured value corresponding to the O.sub.2 content of the waste air evacuated from the reaction vessel, and the throughput rate of the aeration air is controlled as a function of this CO.sub.2 content so that always a maximum CO.sub.2 content is obtained starting from a given minimum air-throughput, the air throughput is increased at certain switching intervals until the CO.sub.2 content reaches a maximum. The air throughput is decreased again after exceeding this maximum when the CO.sub.2 content decreases. Thus, in this known process the air throughput is always controlled such that there is a maximal CO.sub.2 content, while no suggestion of how to predetermine the minimum air-throughput rate itself is provided.
Further, German Patent Application 2,558,255 discloses a process for composting organic waste or sewage sludge wherein the throughput rate of the aeration air flowing through the reaction vessel is controlled such that the O.sub.2 content or the corresponding CO.sub.2 content, respectively, of the waste air leaving the aeration reactor takes a desired value which has been set externally. This desired value thus is a fixed value externally set, which either is not altered during the entire composting process, or can be manually corrected externally by inputting a new desired value.
Finally, German Patent Application 2,500,014 discloses a process for composting organic waste or sewage sludge wherein the throughput rate of the aeration air flowing through the reaction vessel is fixedly set without adjustment by means of an adjustment element. In this process, the O.sub.2 content or CO.sub.2 content, respectively, of the waste air leaving the reaction vessel thus is not considered at all.